How can I set the geometric resolution of a primitive?
Blender 2.8
In Blender 2.8, after adding a UV sphere, a flyout appears on the bottom of the 3D viewport:

I have no idea on how to access that with a keyboard shortcut.
earlier versions
If you press T before adding the UV sphere, you should see the &quot;Transform&quot; panel which allows you to set the  segments and rings.

If you already have the UV sphere and want to modify it instead of creating a new one from scratch, you could use the Subdivision Surface (&quot;Subsurf&quot;) modifier.